328 research outputs found
New algorithm of the high-temperature expansion for the Ising model in three dimensions
New algorithm of the finite lattice method is presented to generate the
high-temperature expansion series of the Ising model. It enables us to obtain
much longer series in three dimensions when compared not only to the previous
algorithm of the finite lattice method but also to the standard graphical
method. It is applied to extend the high-temperature series of the simple cubic
Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25}
to beta^{32} for the magnetic susceptibility.Comment: 3 pages, Lattice2002(spin
Specific heat and high-temperature series of lattice models: interpolation scheme and examples on quantum spin systems in one and two dimensions
We have developed a new method for evaluating the specific heat of lattice
spin systems. It is based on the knowledge of high-temperature series
expansions, the total entropy of the system and the low-temperature expected
behavior of the specific heat as well as the ground-state energy. By the choice
of an appropriate variable (entropy as a function of energy), a stable
interpolation scheme between low and high temperature is performed. Contrary to
previous methods, the constraint that the total entropy is log(2S+1) for a spin
S on each site is automatically satisfied. We present some applications to
quantum spin models on one- and two- dimensional lattices. Remarkably, in most
cases, a good accuracy is obtained down to zero temperature.Comment: 10 pages (RevTeX 4) including 11 eps figures. To appear in Phys. Rev.
Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices
We present an efficient algorithm for computing the partition function of the
q-colouring problem (chromatic polynomial) on regular two-dimensional lattice
strips. Our construction involves writing the transfer matrix as a product of
sparse matrices, each of dimension ~ 3^m, where m is the number of lattice
spacings across the strip. As a specific application, we obtain the large-q
series of the bulk, surface and corner free energies of the chromatic
polynomial. This extends the existing series for the square lattice by 32
terms, to order q^{-79}. On the triangular lattice, we verify Baxter's
analytical expression for the bulk free energy (to order q^{-40}), and we are
able to conjecture exact product formulae for the surface and corner free
energies.Comment: 17 pages. Version 2: added 4 further term to the serie
Higher orders of the high-temperature expansion for the Ising model in three dimensions
The new algorithm of the finite lattice method is applied to generate the
high-temperature expansion series of the simple cubic Ising model to
for the free energy, to for the magnetic
susceptibility and to for the second moment correlation length.
The series are analyzed to give the precise value of the critical point and the
critical exponents of the model.Comment: Lattice2003(Higgs), 3 pages, 2 figure
Low temperature expansion for the 3-d Ising Model
We compute the weak coupling expansion for the energy of the three
dimensional Ising model through 48 excited bonds. We also compute the
magnetization through 40 excited bonds. This was achieved via a recursive
enumeration of states of fixed energy on a set of finite lattices. We use a
linear combination of lattices with a generalization of helical boundary
conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767
The synaptic ribbon is critical for sound encoding at high rates and with temporal precision.
We studied the role of the synaptic ribbon for sound encoding at the synapses between inner hair cells (IHCs) and spiral ganglion neurons (SGNs) in mice lacking RIBEYE (RBEKO/KO). Electron and immunofluorescence microscopy revealed a lack of synaptic ribbons and an assembly of several small active zones (AZs) at each synaptic contact. Spontaneous and sound-evoked firing rates of SGNs and their compound action potential were reduced, indicating impaired transmission at ribbonless IHC-SGN synapses. The temporal precision of sound encoding was impaired and the recovery of SGN-firing from adaptation indicated slowed synaptic vesicle (SV) replenishment. Activation of Ca2+-channels was shifted to more depolarized potentials and exocytosis was reduced for weak depolarizations. Presynaptic Ca2+-signals showed a broader spread, compatible with the altered Ca2+-channel clustering observed by super-resolution immunofluorescence microscopy. We postulate that RIBEYE disruption is partially compensated by multi-AZ organization. The remaining synaptic deficit indicates ribbon function in SV-replenishment and Ca2+-channel regulation
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